Warm up

Estimate the following radicals.

1. 2. 3.

4. 5. 6.

80 38 104

13 52 125

8.9 6.1 10.2

3.6 7.3 11.2

Lesson 11.2 Simplifying Radical Expressions

(Numbers Only)

SWBAT: Multiply and simplify radical expressions containing numbers

Review: The parts of a radical

7 4x

The radical bar. Kind of like a division sign with a tail

The Radicand. The “stuff” underneath the radical bar, can be numbers or variables or both.

The index. The number above the “tail.” Normally it is a 2 and isn’t even written.

How to Simplify RadicalsThe radical bar is kind of like “math” prison.

Anyone that can, wants to get out of prison.

But there are guards, so in order to bust out of the joint the numbers always break out

in groups.

The size of the group depends on the number of guards.

Let the escape begin…

Step 1: Figure out the number of “guards” in the prison. The index is the

number of guards.

How many guards are there in the following problems?

12 7 64 8 3 18

2 72 3

Step 2: Figure out how many prisoners (the radicand) are going to escape. In order to do this we must create a factor tree to determine how

many groups there are

The number of guards determine the number of prisoners in each group trying to escape.

Simplifying Radicals with Numbers.

Simplify the following.

Step one, break the number down into a factor tree.

Step two: Circle any pairs.The pairs bust out of the klink.

20

20

2 10

2 5

The Great EscapeSo here is how it goes down. Those 3 prisoners, not very

smart, see that there are only two guards and think, hey, two of us can charge the guards and get away.

So two of the prisoners (the pair of 2’s) go charging at the guards…but, only one gets away. One gets caught and is never seen or heard from again. And the third guy (the 5), since he didn’t have a partner to charge the guards

with, he’s left to rot in prison.

That’s what happens when you lead a life of crime.

So… which is really just…

so it ends up like this…

2 2 5

20

This guy gets awayThis guy gets caught and is never heard from again

This guy didn’t have a partner and so is left in prison

2 5The guy that got away The guy left in

prison

But teacher, teacher, what happens to the other guy?

He’s Dead, gone, went bye bye, won’t see him again!

Another Example

Simplify the following:

Step 1: Make a factor tree

So that leaves:

Which is:

140

140

14 10

2 7 52

2 7 5

2 35

Your Turn!

Simplify the following:1.

2.

3.

4.

44

64

56

250

2 11

8

2 14

5 10

Summary: To simplify radicals I must …

Homework: Radical Worksheet